Problem: Find the distance between the planes $x - 3y + 3z = 8$ and $2x - 6y + 6z = 2.$
Solution: We can write the equation of the second plane as $x - 3y + 3z = 1.$  Note that $(1,0,0)$ is a point on this plane.  (Also, note that both plane have the same normal vector, so they are parallel.)

Therefore, from the formula for the distance between a point and a plane, the distance between the two planes is
\[\frac{|1 - 3 \cdot 0 + 3 \cdot 0 - 8|}{\sqrt{1^2 + (-3)^2 + 3^2}} = \boxed{\frac{7 \sqrt{19}}{19}}.\]